Another way to solve this problem, as for many problems like this, is to look for a pattern.
You will notice than when 7 is multipled by 7 (=49) it ends in a 9.. then multiplied by 7 again, the number ends in a 3, then multipled by 7 again the number ends in a 1, multiplied by 7 again the number ends in a 7.. and then the pattern continues - 9, 3, 1, 7 , 9, 3, 1, 7, etc... All we need to know is this ones digit because it will tell us what the remainder will be.
Thus, since 342 ends in a 2, we can test each ones digit from above to find the remainder.. 9/2 = remainder 1, 3/2 = remainder 1, 1/2(doesnt count so move on, 7/2 = remainder 1.. We can see from this that the remainder will be 1
The answer is
A
I hope this helps
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